Question

Investigate the construction of a triangle in these portfolio activities. Use what you
have learned about the Triangle Angle Sum Theorem and the Triangle Inequality
Theorem to create your submissions. Record your answers below.
Question 1
Find three objects (sticks, utensils, yarn, toys, books, etc.) that could represent
the sides of a triangle. Can you make a triangle with these three objects? Use the
Triangle Inequality Theorem explain why or why not.
(a) measurements of each object:
(b) Application of Triangle Inequality Theorem:

Answer 1

To investigate whether three objects can form a triangle, we need to use the Triangle Inequality Theorem, which states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following conditions must be met:

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

In this exercise, I'll select three objects and apply the theorem.

### Question 1

#### (a) Measurements of Each Object

1. **Object 1 (Stick)**: Length = 5 cm
2. **Object 2 (Stick)**: Length = 7 cm
3. **Object 3 (Stick)**: Length = 10 cm

#### (b) Application of Triangle Inequality Theorem

Now, we will check the conditions of the Triangle Inequality Theorem:

1. \(5 + 7 > 10\)

- Calculation: \(12 > 10\) (True)

2. \(5 + 10 > 7\)

- Calculation: \(15 > 7\) (True)

3. \(7 + 10 > 5\)

- Calculation: \(17 > 5\) (True)

Since all three conditions of the Triangle Inequality Theorem are satisfied, we can conclude that these three objects can indeed form a triangle.

**Conclusion**: Yes, we can make a triangle with these three objects, as they meet the criteria set by the Triangle Inequality Theorem.